Sample rate doubling using alternating ADCs

ABSTRACT

One embodiment of the invention includes a system comprising an analog baseband signal input, a conversion circuit with N Analog to Digital Converters (ADCs) operable to receive the analog baseband signal, and a Finite Impulse Response (FIR) filter operable to receive outputs of the N ADCs and to produce a digital representation of the analog baseband signal corrected for a mismatch in the N ADCs.

BACKGROUND OF THE INVENTION

In the filed of signal receivers, converting both broadband and basebandanalog signals to digital signals involves an inherent trade-off betweenAnalog to Digital Converter (ADC) sample rate and accuracy. Designersare faced with the choice of using a faster ADC that may lack a highdegree of accuracy or using a lower sample rate ADC that has moreaccuracy. Oftentimes, the choice is made for the designer because thefrequency of the received signal, F_(signal), dictates the minimumsample rate, F_(sample), that must be used to avoid aliasing. Typicallythis would be 2F_(signal)=F_(sample).

One approach that has seen some success in the conversion ofIntermediate Frequency (IF) signals is to use alternating ADCs that eachsample at half of the desired sample rate (assuming that the bandwidthof the IF signal is less than or equal to double the first Nyquistintervals of each of the ADCs). First, the IF signal is converted intoone In-Phase (I) and one Quadrature (Q) signal (i.e., I/Q basebandsignals). The I and Q signals are then each digitized by one of a pairof alternating ADCs that sample at one half F_(sample). Distortion isadded to the signals because of non-ideal and non-matching frequencyresponses of the two ADCs. In fact, the frequency response mismatch ofthe two ADCs can eliminate much of the advantage of a two ADC systemover a single ADC system.

In one solution, the I and Q signals are then processed by localoscillators that multiply the I digitized signal by a sequence of [1,−1, 1 . . . ] and multiply the Q digitized signal by a sequence of [j,−j, j . . . ]. This results in a clean, conceptual separation of I and Qsamples between the real and imaginary paths for subsequent processing.The frequency response corruption of each ADC can then be associatedwith the real or imaginary data streams. A single Finite ImpulseResponse (FIR) filter is used to eliminate the corruption of the datapaths, with the output of the filter being reassembled into one digitalsignal that includes all of the information of the original analogsignal.

The conceptual separation of distortion into real and imaginarycomponents provides the key to understanding that a single FIR filtercan be implemented to correct for the frequency response mismatch of thetwo ADCs. However, the IF signal solution does not necessarily lead to asolution for correcting for frequency response mismatch between two ADCsin a system that digitizes a single analog baseband input signal. Thisis because a single analog baseband input signal cannot be separatedinto real and imaginary components.

BRIEF SUMMARY OF THE INVENTION

One embodiment of the invention includes a system comprising an analogbaseband signal input, a conversion circuit with N Analog to DigitalConverters (ADCs) operable to receive the analog baseband signal, and aFinite Impulse Response (FIR) filter operable to receive outputs of theN ADCs and to produce a digital representation of the analog basebandsignal corrected for a mismatch in the N ADCs.

In another embodiment of the invention, correcting for frequencyresponse mismatch in a dual-ADC system is accomplished by splitting thesignal into even and odd paths, wherein the odd path signal is subjectedto a time delay. The two paths are digitized by separate ADCs to produceeven and odd digital representation components of the original analogbaseband input signal. The even and odd components contain distortionfrom the frequency response mismatch between the two ADCs. To correctfor the mismatch, the components are then input into a single FIR filterthat applies 2×2 matrix filter taps. The result is corrected even andodd components that can be reassembled into a single digital signal thatincludes all of the information of the original analog baseband inputsignal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of one embodiment of the invention forperforming sample rate doubling using alternating ADCs;

FIG. 2 is a flowchart of one embodiment of the invention for correctingfor ADC mismatch;

FIG. 3 is an illustration of one embodiment of the invention forperforming sample rate doubling using alternating ADCs; and

FIG. 4 is an illustration of one embodiment of the invention forperforming sample rate tripling using three ADCs.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is an illustration of one embodiment of the invention in whichsystem 100 is shown for performing sample rate doubling usingalternating Analog to Digital Converters (ADCs). In this example, input120 is an analog baseband signal that is provided to circuit 101 fordigital conversion. As with any circuit, circuit 110 includes an impulseresponse, illustrated by h(t) 101. Impulse response 101 is the responsefor ADCs 104 and 105, delay 102, and additional components of thecircuit that are not shown. Although impulse response 101 is determinedby the characteristics of the various components of circuit 110, it isillustrated as a separate component of circuit 110 for simplicity.

Input 120 is provided to circuit 110 and split into two paths. The toppath leads to ADC 104. The bottom path leads to delay 102 and ADC 105.In this embodiment, ADCs 104 and 105 are both run by clock 103.Accordingly, while both paths convert signal 120 into a digital signal,the lower path subjects input 120 to a time delay. Conceptually, ADCs104 and 105 are alternating so that, in a given clock cycle, togetherthey produce a set of samples corresponding to one delay of zero and onedelay of T/2. The result is that ADCs 104 and 105 operate respectivelyto produce even and odd digital representation components 106 of analoginput signal 120. Neither component by itself represents all of theinformation contained in analog baseband signal input 120 because ADCs104 and 105 each perform undersampling. This allows sampling where the abandwidth of the analog baseband input signal is wider than the Nyquistband of either of the individual ADCs. However, taken together,components 106 will represent all of the information in analog basebandsignal input 120 as long as each ADC 104 and 105 samples input 120 atleast at half of the desired sample frequency.

Ideally, ADCs 104 and 105 sample analog baseband signal input 120 atexactly the same time and operate with exactly the same parameters.Practical embodiments, however, show some degree of frequency responsemismatch. The result of frequency response mismatch is that whencomponents 106 are assembled into a single digital signal, there will besome amount of information distortion. Therefore, the accuracy of thedigital representation will be degraded.

Impulse response 101 includes the frequency response mismatch betweenADCs 104 and 105, and it is possible to use impulse response 101 todesign filter 130 to effectively correct for the mismatch. System 100includes Finite Impulse Response (FIR) filter 130 operable to receiveoutputs 106 of ADCs 104 and 105, and to produce digital representation107 of analog baseband signal input 120 corrected for the mismatchbetween ADCs 104 and 105.

A problem encountered in correcting for the frequency response mismatchbetween alternating ADCs is how to design a filter, such as FIR filter130, that can account for the fact that each of the digitalrepresentation components 106 are not complete representations of analogbaseband signal input 120. It is not as simple as putting a singlefilter behind each ADC 104 and 105. A single filter that receives onlythe even or odd components will not have enough information to correctlyfilter the component because there is an infinite combination of firstand second Nyquist interval signals that could combine to produce thesame sequence of samples that are found in that component. Therefore,the filter that is needed is one that receives and conditions both theeven and odd sampled components. In other words, the filtercross-couples both the even and odd components to compute the linearcombination of all samples to produce the correct even samples and thelinear combination of all samples to produce the correct odd samples.FIR filter 130 provides such a solution by incorporating a sequence of2×2 matrix filter taps that are each computed using even and oddcomponents of system impulse response 101 and are each applied to evenand odd components of representation 106.

The process of calculating the correct FIR filter taps will now beexplored. The following equations treat each pair of even and odddigital representation components 106 as a two-element vector.Performing the calculations with vectors and matrices is done for theconvenience of the notation, since system 100 uses alternating ADCs 104and 105. Those of skill in the art will understand that the calculationscan also be performed with time-varying, piecemeal functions thatrepresent the alternating of ADCs 104 and 105.

The desired signal processing of analog baseband signal input signal120, x(t), is given in Equation 1.

$\begin{matrix}{y_{n} = \begin{bmatrix}{{x(t)} \otimes {g(t)}} \\{{x( {t + {T\text{/}2}} )} \otimes {g(t)}}\end{bmatrix}_{t = {n\; T}}} & (1)\end{matrix}$where T is the sampling period of each ADC 104 and 105, and g(t) is theimpulse response of the desired filtering to be applied to the signal.This response, g(t), has a bandwidth of less than 1/T in order for thecomposite sample rate to eliminate aliasing. This may be implemented,for example, as a flat pass band for the first Nyquist interval of x(t)with a transition band that rolls off rapidly to filter out frequenciesof the second Nyquist interval. The filtering represented by g(t) may bea user's ideal analog-to-digital conversion of analog baseband signalinput signal 120, and it is usually chosen by the user.

However, the actual output signal 106 from circuit 110 (a dual-ADC frontend) is represented by Equation 2:

$\begin{matrix}{x_{n} = \begin{bmatrix}{{x(t)} \otimes {h_{1}(t)}} \\{{x(t)} \otimes {h_{2}(t)}}\end{bmatrix}_{t = {n\; T}}} & (2)\end{matrix}$where h₁(t) is the impulse response from the input connector througheven-sample ADC 104, and h₂(t) is the impulse response from the inputconnector through odd-sample ADC 105. Splitting impulse response 101into h₁(t) and h₂(t) is a way of adapting response 101 to the vectornotation used herein. It also expresses that each of the two paths haveindividual impulse responses. It should be noted that, similar toEquation 1, the right hand side represents an array of discrete samplevalues. Further, the bandwidth of h₁(t) and h₂(t) is assumed to be lessthan 1/T.

The goal is to determine the appropriate calibration filter response,q_(n), of filter 130. Equation 3 represents the relationship of q_(n),y_(n), and x_(n). As shown below, Equation 3 can be manipulated tocalculate q_(n).y_(n)=q_(n)

x_(n)  (3)

Equation 3 can be rewritten as Equation 4 by explicitly writing out theconvolution integrals:

$\begin{matrix}{\begin{bmatrix}{\int_{\tau = {- \infty}}^{\infty}{{x(\tau)}{g( {{n\; T} - \tau} )}{\mathbb{d}\tau}}} \\{\int_{\tau = {- \infty}}^{\infty}{{x( {{\tau 1} + {T\text{/}2}} )}{g( {{n\; T} - \tau^{1}} )}\ {\mathbb{d}\tau^{1}}}}\end{bmatrix} = {q_{n} \otimes \begin{bmatrix}{\int_{\tau = {- \infty}}^{\infty}{{x(\tau)}{h_{1}( {{n\; T} - \tau} )}{\mathbb{d}\tau}}} \\{\int_{\tau = {- \infty}}^{\infty}{{x(\tau)}{h_{2}( {{n\; T} - \tau} )}{\mathbb{d}\tau}}}\end{bmatrix}}} & (4)\end{matrix}$where the new dummy integration variable τ=τ′+½. This does not changethe integration result because of the infinite bounds. Similarly, thediscrete sample data convolution summation can be written outexplicitly, as in Equation 5.

$\begin{matrix}{\begin{bmatrix}{\int_{\tau = {- \infty}}^{\infty}{{x(\tau)}{g( {{n\; T} - \tau} )}{\mathbb{d}\tau}}} \\{\int_{\tau = {- \infty}}^{\infty}{{x(\tau)}{g( {{n\; T} + {T\text{/}2} - \tau} )}\ {\mathbb{d}\tau}}}\end{bmatrix} = {\sum\limits_{\tau = {- \infty}}^{\infty}\;{q_{m}\begin{bmatrix}{\int_{\tau = {- \infty}}^{\infty}{{x(\tau)}{h_{1}( {{( {n - m} )T} - \tau} )}{\mathbb{d}\tau}}} \\{\int_{\tau = {- \infty}}^{\infty}{{x(\tau)}{h_{2}( {{( {n - m} )T} - \tau} )}{\mathbb{d}\tau}}}\end{bmatrix}}}} & (5)\end{matrix}$

The integration and summation can now be reordered. Also, since thedummy integration variable is the same for both elements of each vector,the integration can be performed with the integrand being a scalarmultiplied by a vector, as in Equation 6.

$\begin{matrix}{{\int_{\tau = {- \infty}}^{\infty}{{{x(\tau)}\begin{bmatrix}{g( {{n\; T} - \tau} )} \\{g( {{n\; T} + {T\text{/}2} - \tau} )}\end{bmatrix}}\ {\mathbb{d}\tau}}} = {\int_{\tau = {- \infty}}^{\infty}{{x(\tau)}{\sum\limits_{\tau = {- \infty}}^{\infty}\;{{q_{m}\begin{bmatrix}{h_{2}( {{( {n - m} )T} - \tau} )} \\{h_{2}( {{( {n - m} )T} - \tau} )}\end{bmatrix}}\ {\mathbb{d}\tau}}}}}} & (6)\end{matrix}$

It is desirable to enforce Equation 6 to hold true for any arbitraryinput signal x(t) and for all values of n and t. Accordingly, this isrelationship is expressed as Equation 7.

$\begin{matrix}{\begin{bmatrix}{g( {{n\; T} - \tau} )} \\{g( {{n\; T} + {T\text{/}2} - \tau} )}\end{bmatrix} = {\sum\limits_{\tau = {- \infty}}^{\infty}\;{q_{m}\begin{bmatrix}{h_{2}( {{( {n - m} )T} - \tau} )} \\{h_{2}( {{( {n - m} )T} - \tau} )}\end{bmatrix}}}} & (7)\end{matrix}$

Because of the bandwidth limits on the filters, the impulse responses g,h₁, and h₂, are all fully specified with time samples spaced atintervals of T/2. Thus, the constraint above need only be evaluated atdiscrete time points t=0 and t=T/2. The constraint at both of these timepoints can be written into a single matrix equation, as in Equation 8.

$\begin{matrix}{\lbrack {\begin{matrix}{g( {n\; T} )} \\{g( {{n\; T} + {T\text{/}2}} )}\end{matrix}\begin{matrix}{g( {{n\; T} - {T\text{/}2}} } \\{g( {n\; T} )}\end{matrix}} \rbrack = {\sum\limits_{\tau = {- \infty}}^{\infty}\;{q_{m}\lbrack {\begin{matrix}{h_{1}( {( {n - m} )T} )} \\{h_{2}( {( {n - m} )T} )}\end{matrix}\begin{matrix}{h_{1}( {{( {n - m} )T} - {T\text{/}2}} )} \\{h_{2}( {{( {n - m} )T} - {T\text{/}2}} )}\end{matrix}} \rbrack}}} & (8)\end{matrix}$

It is now useful to define the following matrices in Equations 9 and 10.

$\begin{matrix}{h_{n} = \lbrack {\begin{matrix}{{h_{1}( {n\; T} )}\mspace{14mu}} \\{{h_{2}( {n\; T} )}\mspace{14mu}}\end{matrix}\begin{matrix}{h_{1}( {{n\; T} - {T\text{/}2}} )} \\{h_{2}( {{n\; T} - {T\text{/}2}} )}\end{matrix}} \rbrack} & (9)\end{matrix}$

$\begin{matrix}{g_{n} = \lbrack {\begin{matrix}{g( {n\; T} )} \\{g( {{n\; T} + {T\text{/}2}} )}\end{matrix}\begin{matrix}{g( {{n\; T} - {T\text{/}2}} } \\{g( {n\; T} )}\end{matrix}} \rbrack} & (10)\end{matrix}$

The desired set of coefficient matrices, q_(m), is found by solving amatrix convolution equation, as in Equation 11.

$\begin{matrix}{g_{n} = {\sum\limits_{\tau = {- \infty}}^{\infty}\;{q_{m}\mspace{14mu} h_{n - m}}}} & (11)\end{matrix}$

This solution can be approached by transforming the matrices to thefrequency domain in order to avoid performing convolution. The length ofthe transform, N, should be long enough to encompass the completeimpulse responses g, h₁, and h₂.

$\begin{matrix}{{\sum\limits_{n = 0}^{N - 1}\;{{\mathbb{e}}^{\frac{{- {j2\pi}}\; k\; n}{N}}g_{n}}} = {\sum\limits_{\tau = {- \infty}}^{\infty}\;{q_{m}{\mathbb{e}}^{\frac{{- {j2\pi}}\; k\; m}{N}}{\sum\limits_{n = 0}^{N - 1}\;{{\mathbb{e}}^{\frac{{- {j2\pi}}\;{k{({n - m})}}}{N}}h_{n - m}}}}}} & (12)\end{matrix}$

Substitute p=n−m. This changes the limits on the rightmost summation.

$\begin{matrix}{{\sum\limits_{n = 0}^{N - 1}\;{{\mathbb{e}}^{\frac{{- {j2\pi}}\; k\; n}{N}}g_{n}}} = {\sum\limits_{\tau = {- \infty}}^{\infty}\;{q_{m}{\mathbb{e}}^{\frac{{- {j2\pi}}\; k\; m}{N}\;}{\sum\limits_{p = {- m}}^{N - 1 - m}\;{{\mathbb{e}}^{\frac{{- {j2\pi}}\; k\; p}{N}}h_{p}}}}}} & (13)\end{matrix}$

The limits on the rightmost summation may be adjusted to be independentof m if the value being summed is periodic in N. This is accomplished byreplacing h with h′ which is a cyclic version of the finite durationimpulse response, as expressed in Equation 14.h′_(p)=h _(p mod N)  (14)

Making this substitution and limiting the number of filter taps givesEquation 15. Note that the filter taps are non-zero only in the range 0through N−1, such that the non-zero range is implemented cyclically inEquation 15. Thus, N must be chosen to be large enough to encompass thecomplete compensation filter impulse response, q_(m). In general thiswill be somewhat longer than the g and h responses. Making N too smallwill limit the degrees of freedom needed to produce a good calibrationresponse.

$\begin{matrix}{{\sum\limits_{n = 0}^{N - 1}\;{{\mathbb{e}}^{\frac{{- {j2\pi}}\; k\; n}{N}}g_{n}}} = {\sum\limits_{m = 0}^{n - 1}\;{{\mathbb{e}}^{\frac{{- {j2\pi}}\; k\; m}{N}\;}{q\;}_{m}{\sum\limits_{p = 0}^{N - 1}\;{{\mathbb{e}}^{\frac{{- {j2\pi}}\; k\; p}{N}}h_{p}^{\prime}}}}}} & (15)\end{matrix}$

Each of the summations in Equation 15 represents a Fourier transform.Using capitals letters to denote the transforms yields Equation 16.G_(k)=Q_(k)H_(k)  (16)

Equation 16 can be manipulated to solve for the frequency response ofthe desired calibration filter, as in Equation 17. Note that thetransformed matrix elements are complex, so the indicated multiplicationrequires complex operations. Also, note that since the original timedomain matrices are real, the transformed matrices have conjugatesymmetry with respect to the k index modulo N. This fact can be utilizedto reduce the variable storage and computation time.Q_(k)=G_(k)H{overscore (_(k) ¹)}  (17)

To get the impulse response now requires taking the inverse Fouriertransform, as in Equation 18.

$\begin{matrix}{q_{m} = {\sum\limits_{k = 0}^{N - 1}{{\mathbb{e}}^{\frac{{- {j2\pi}}\;{km}}{N}}Q_{k}}}} & (18)\end{matrix}$

The output, q_(m), is a sequence of N 2×2 matrices that is cycledthrough continuously by FIR filter 130. Each of the individual matricesis a filter tap to be used by FIR filter 130 to correct for the mismatchof ADCs 104 and 105. As mentioned above with regard to Equation 6, q_(m)will hold for other signals that do not exceed the Nyquist frequency,1/T.

FIG. 2 is a flowchart embodiment showing method 200 for correcting forADC mismatch. Process 201 determines h₁(t) and h₂(t). Various ways existto determine h₁(t) and h₂(t). For example, a well-controlled, known testinput may be used as the analog baseband signal input for circuit 110(FIG. 1). The outputs of ADCs 104 and 105 are sampled and recorded atintervals of T/2. Substituting these values into Equation 2 above willyield a relation that may be manipulated to solve for discrete values ofh₁(t) and h₂(t). Impulse responses h₁(t) and h₂(t) represent not onlythe impulse response of circuit 110, but also the time offset errorbetween ADCs 104 and 105.

Process 202 selects a desired frequency response, g(t). The desiredfrequency response is one wherein the ADCs have little or no frequencyresponse mismatch, and it may even be mathematically ideal,theoretically eliminating mismatch totally.

Process 203 samples and records the desired frequency response atintervals of T/2. This step puts the frequency response into a discreteform that can be used in Equations 4–18 above.

Process 204 forms the array of matrices defined in Equations 9 and 10,using the sampled, recorded responses from blocks 201 and 203.

Process 205 performs the Fourier Transforms of Equation 13 on thematrices of Equations 9 and 10, wherein the array of individual matrixelements is treated as a real data sequence. This yields the frequencydomain matrices of Equation 16.

Process 206 inverts each H matrix array in the array to perform themultiplication of Equation 17. This step is performed matrix-by-matrixacross the entire array of matrices.

Process 207, performs the inverse Fourier Transform of Equation 18 onthe results of the step of block 206. The array of individual matrixelements is treated as a complex data sequence for the inverse FourierTransform. This step yields the array of vectors, q_(m).

Process 208 implements q_(m) in FIR filter 130 to correct for frequencyresponse mismatches between ADCs 104 and 105 (all of FIG. 1).Accordingly, any analog baseband input signal 120, which does not exceedthe Nyquist frequency of 1/T, may be input into circuit 110, conditionedby filter 130, and output as an accurate digital representation 107 ofthat original analog input signal 120.

FIG. 3 is one embodiment of system 300 for performing sample ratedoubling using alternating ADCs. It is similar to system 100, butinstead of employing a delay element (such as element 102 of FIG. 1),system 300 uses advanced (or, alternatively, delayed) clock 301. Theresult is the same as in system 100—even and odd digital representationcomponents 106 are produced at the outputs of ADCs 104 and 105. Theinvention is not limited to any particular process of producing even andodd digital representation components of an input analog basebandsignal, and other alternative embodiments are within the scope of theinvention. Even and odd digital representation components are oneexample of a more general complementary relationship between sampleddigital components when exactly two sampled components exist. Asexplained below, the complementary relationship may be generalized toencompass embodiments that include more than two sampled digitalcomponents.

The above example embodiments utilize an FIR filter with 2×2 matrixtaps. The present invention, however, may be expanded to coverembodiments wherein the filter employs larger matrix taps.

FIG. 4 is one embodiment of system 400 for performing sample ratetripling using three ADCs 401–403. Just as in the last examples, whereinthe rate of sampling of a circuit is doubled by using two ADCs, the rateof sampling may be tripled by employing three ADCs in the arrangementshown. ADC 401 has zero delay at its input, while ADC 402 has T/3 delay405 to its input, and ADC 403 has 2T/3 delay 405 to its input. ADCs401–403 are conceptually cyclic, so that, in a given clock cycle,together they produce a set of samples that includes a sample delayed byzero, a sample delayed by T/3, and a sample delayed by 2T/3.

It can be seen that, rather than using even and odd digitalrepresentation components (such as components 106 of FIG. 1), system 400uses three complementary components 406 that are delayed in a manneranalogous to the delay in the two-ADC embodiments above. FIR filter 407,in this case, is a 3×3 filter. The computation of the matrix filter tapsis similar to that of the 2×2 matrix taps, such that Equations 3, 11,and 16–18 hold true, however the intermediate calculation equations mustbe adapted for use of 3-element vectors and 3×3 matrices.

Other multiple-ADC embodiments are possible and are within the scope ofthe invention. In fact, the number of ADCs may be increased to N (“N” isnot necessarily the same as that used in Equation 14, above), whereinthe FIR filter applies N×N matrix taps to complementary digitalrepresentation components to correct for mismatch of the ADCs.

It should be noted that the computation of the taps of filter 130 isperformed using matrices and vectors, effectively representing the evenand odd samples as pairs that have been taken simultaneously and thefilter coefficients as sets of four coefficients that are appliedsimultaneously. From another point of view, ADCs 104 and 105 (of FIG. 1)may be seen as taking samples at alternating times during time periods,T, with filter 130 (of FIG. 1) applying coefficients to even and oddsamples at alternating times. This can be represented as time-varying,piecemeal equations, wherein filter 130 applies one set of coefficientsduring certain times to the even components and other sets ofcoefficients at other times to the odd components. Applications usingeither view are within the scope of the various embodiments, and thoseof skill in the art will understand that the two approaches aremathematically equivalent.

Although the present invention and its advantages have been described indetail, it should be understood that various changes, substitutions andalterations can be made herein without departing from the invention asdefined by the appended claims. Moreover, the scope of the presentapplication is not intended to be limited to the particular embodimentsof the process, machine, manufacture, composition of matter, means,methods and steps described in the specification. As one will readilyappreciate from the disclosure, processes, machines, manufacture,compositions of matter, means, methods, or steps, presently existing orlater to be developed that perform substantially the same function orachieve substantially the same result as the corresponding embodimentsdescribed herein may be utilized. Accordingly, the appended claims areintended to include within their scope such processes, machines,manufacture, compositions of matter, means, methods, or steps.

1. A method for digitizing an analog baseband signal comprising:receiving the analog baseband signal into a conversion circuit with NAnalog to Digital Converters (ADCs); and correcting for a mismatch inthe N ADCs by applying a Finite Impulse Response (FIR) filter to theoutputs of the ADCs, wherein the FIR filter includes a plurality of N×Nmatrix filter taps.
 2. The method of claim 1 further comprising:determining and sampling a transfer function of the conversion circuit;selecting and sampling a desired frequency response; forming an array ofmatrices of the samples of the transfer function and an array ofmatrices of the samples of the desired frequency response; performing aFourier Transform on said arrays; multiplying the transformed array ofmatrices of samples of the desired frequency response with an array ofinverted matrices of samples of the transfer function, matrix-by-matrix;performing an inverse Fourier Transform on the array of matrices thatresults from the multiplying step; and implementing the result of theinverse Fourier Transform in the FIR filter.
 3. The method of claim 2wherein determining and sampling a transfer function of the conversioncircuit comprises: inputting a known signal to the circuit and recordingthe output thereof; determining the transfer function from the outputand the known input; and generating discrete samples of the transferfunction.
 4. The method of claim 2 wherein the desired frequencyresponse is a flat pass band for a first Nyquist interval of the analogbaseband signal with a transition band that rolls off rapidly.
 5. Themethod of claim 1 wherein said conversion circuit includes two ADCs, andthe FIR filter includes 2×2 matrix filter taps.
 6. The method of claim 1wherein said conversion circuit includes three ADCs, and the FIR filterincludes 3×3 matrix filter taps.
 7. The method of claim 1 furthercomprising outputting a digital signal that is a representation of theanalog baseband signal.
 8. The method of claim 1 wherein receiving ananalog baseband signal into a conversion circuit comprises splitting theanalog baseband signal into N complementary paths, each path including adifferent time delay and one of the N ADCs.
 9. A system comprising: ananalog baseband signal input; a conversion circuit with N Analog toDigital Converters (ADCs) operable to receive the analog basebandsignal; and a Finite Impulse Response (FIR) filter operable to receiveoutputs of the N ADCs and to produce a digital representation of theanalog baseband signal corrected for a mismatch in the N ADCs, whereinthe FIR filter applies filter taps to the outputs of the ADCs, andwherein the filter taps are computed from a transfer function of thecircuit and a desired frequency response.
 10. The system of claim 9wherein a bandwidth of the analog baseband input signal is wider than aNyquist band of any of the individual ADCs.
 11. The system of claim 10wherein the FIR filter applies 3×3 matrix taps to the outputs of theADCs.
 12. The system of claim 10 wherein the conversion circuit includesa non-zero delay element before one of the ADCs.
 13. The system of claim9 wherein the mismatch includes a frequency response mismatch and a timeoffset error.
 14. The system of claim 9 wherein the conversion circuitincludes a delayed clock coupled to one of the ADCs.
 15. A conversioncircuit comprising: means for producing complementary digitalrepresentation components of an analog baseband signal; and means forapplying a plurality of filter taps to the complementary components forcorrecting for a mismatch in said producing means, wherein saidcorrecting means comprises a Finite Impulse Response (FIR) filter forapplying N×N matrix filter taps to the outputs of a plurality of ADCs.16. The system of claim 15 wherein said producing means comprises: aplurality of Analog to Digital Converters (ADCs), each of said ADCsarranged for receiving the analog baseband signal with a differentdelay.
 17. The system of claim 15 wherein said producing means comprisestwo ADCs producing even and odd digital representation components ofsaid analog baseband signal.
 18. The system of claim 15 wherein saidproducing means comprises a transfer function that includes themismatch.